You didn't say whether the patient was male or female, and that's probably important as I would think there might be slightly different things you could do depending on gender.
But generally, going along with what has already been said:
1) Pay attention to undressing of the patient. They might be more embarrassed with sequential undressing as JDS suggested. Or depending on patient, it might be better to strip them down right away. I think it really depends.
2) You help to undress them. If the patient pulls down their own shorts or panties, they might feel that they are still (ever so slightly) in control. If YOU are the one to pull them down, it might be more embarrassing.
3) An audience. To truly embarrass someone, it's better with an audience. It could be their friend, a "nurse" that is assisting you, a group of med students (great idea JT), etc.
4) Positioning. Strive to put the patient into embarrassing positions. For example, don't do their genital exam lying on the exam table. Make them stand in front of you, feet parted with their hands behind their head, while you sit before them at eye-level with their genitals. Much better. Another example: Don't just have the patient bend over the exam table for a quick prostate exam. Make them get on the table on their hands and knees so you can perform a proper (and thoroughly embarrassing) rectal exam on them.
5) Questions. Ask lots and lots of embarrassing ones. Ask about their frequency of bowel movements. Ask about their sexual history. You get the idea.
6) Make them assist in their own exam. Request that they hold their penis out of the way while you examine their testicles. Make them reach back and spread their own cheeks for the rectal exam.
7) Special clothing. After undressing them, make them put on special clothing for the exam. For example, get some disposable exam shorts that are too small for them. Or provide a jockstrap that they must wear prior to doing some exercises for you (to check their heart rate of course).